Philip L. Marston, Yibing Zhang, and David B. Thiessen, "Observation of the enhanced backscattering of light by the end of a tilted dielectric cylinder owing to the caustic merging transition," Appl. Opt. 42, 412-417 (2003)

Abstract

The scattering of light by obliquely illuminated circular dielectric cylinders was previously demonstrated to be enhanced by a merger of Airy caustics at a critical tilt angle. [Appl. Opt. 37, 1534 (1998)]. A related enhancement is demonstrated here for backward and near-backward scattering for cylinders cut with a flat end perpendicular to the cylinder’s axis. It is expected that merged caustics will enhance the backscattering by clouds of randomly oriented circular cylinders that have appropriately flat ends.

Figures (4)

Geometry of the truncated circular cylinder considered. The ends of the cylinder are perpendicular to the symmetry axis. The wave vector of the illumination is tilted by an angle γ relative to the ends of the cylinder. The actual angle of incidence is i for an illuminated surface point U (where the local cylinder normal is N). The angle of incidence projected onto the base plane is φ, which is smaller than i.

Rays confined to the meridional plane of the cylinder that contribute to the backscattering after the fewest number of reflections. The rays shown are reversible. From Ref. 8, only the region within a distance d = 4a(tan γ)/n′ contributes to the backscattering for the process considered, where n′ is given by Eq. (2). Rays can be backscattered after additional internal reflections; however, the contributions from those rays are relatively weak near tilts given by Eq. (1). This is a consequence of the curvature of the outgoing wave fronts associated with the extra reflections. Angle of refraction ϑ is discussed in Section 5 below.

Experimental configuration for viewing the backscattering from the end of a small tilted cylinder (not drawn to scale). A lens is placed in front of the CCD camera with the CCD array at the focal plane. The backscattering region was also viewed by eye through a telescope. The illumination is horizontal, and the axis of the cylinder is tilted from the vertical by an amount γ by a goniometer. The goniometer measures the rotation about a horizontal axis that is perpendicular to the incident wave vector.

CCD strip records of the near-backward scattering for the value of γ displayed at the left. The strips are shifted vertically in proportion to tilt deviation γc - γ. The evolution as a function of tilt for the calculated Descartes condition is shown as white curves on the right and left sides of the pattern. This evolution was calculated as explained in Section 3. The horizontal scale shows a 1° deviation in the backscattering angle. The CCD camera has been saturated near the brightest region of two of the records.